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11.
12.
Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem. 相似文献
13.
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian.
PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca 相似文献
14.
The quantum action (dynamical) principle is exploited to investigate the nature and origin of the Faddeev–Popov (FP) factor in gauge theories without recourse to path integrals. Gauge invariant as well as gauge non-invariant interactions are considered to show that the FP factor needs to be modified in more general cases and expressions for these modifications are derived. In particular we show that a gauge invariant theory does not necessarily imply the familiar FP factor for proper quantization.
PACS numbers: 11.15.-q; 12.10.-g; 12.15.-y; 12.38.-t 相似文献
15.
We investigate the condition that the charge carried by quantum parametric pumping per cycle is quantized in units of the electron charge e and the role of adiabaticity in charge quantization. Using a driven double-δ-potential model and a Floquet scattering approach, it is found that the quantization phenomenon occurs only at very low frequencies of the oscillating potential and adiabaticity of the potential modulation is crucial for quantization. 相似文献
16.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
17.
A. N. Koryukin 《Algebra and Logic》2003,42(6):387-397
We generalize a well-known two-parameter quantization for the group GL
2(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL
2(k). 相似文献
18.
19.
We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory. 相似文献
20.
The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed.
After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations
of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion
of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations
of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total
trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding
Heisenberg equations.
Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph.
D. Directing Programme of Chinese University, and the Chinese Academy of Sciences. 相似文献